CN107657071A - Based on the power system uncertainty time-domain simulation method for improving sparse probability assignments method - Google Patents

Based on the power system uncertainty time-domain simulation method for improving sparse probability assignments method Download PDF

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CN107657071A
CN107657071A CN201710649712.XA CN201710649712A CN107657071A CN 107657071 A CN107657071 A CN 107657071A CN 201710649712 A CN201710649712 A CN 201710649712A CN 107657071 A CN107657071 A CN 107657071A
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simulation
domain
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time
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林济铿
陈文龙
刘阳升
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Tongji University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The present invention relates to a kind of based on the power system uncertainty time-domain simulation method for improving sparse probability assignments method, mainly including herein below：1）The sparse probability assignments method of improvement based on Kronrod expanding methods of proposition；2）Quantified using sparse the uncertain of probability assignments method progress Power System Time Domain Simulation Under is improved.Compared with prior art, the present invention is in the case where keeping the calculation accuracy condition of uncertain quantized result, it drastically reduce the area required sample size, improve uncertain time-domain-simulation speed, and the Arbitrary distribution of uncertain parameters is can adapt to, wind farm wind velocity in time-domain-simulation, workload demand, failure can be considered the influences of the uncertain parameter for simulation result such as position occur.

Description

Based on the power system uncertainty time-domain simulation method for improving sparse probability assignments method
Technical field
It is dilute based on improving more particularly, to one kind the present invention relates to a kind of power system uncertainty time-domain simulation method Dredge the power system uncertainty time-domain simulation method of probability assignments method.
Background technology
Power System Time Domain Simulation Under analysis is that Electrical Power System Dynamic and Transient Stability Analysis (hereinafter referred to as move temporary characteristic Analysis) main instrument, but it is directed to certainty, the dynamic temporary characteristic of unique performance analysis system mostly so far.With A large amount of grid-connected and electric network composition the complication of regenerative resource, the temporary characteristic of power system dynamic is by more and more uncertain The influence of factor (or event), such as：The uncertainty that wind farm wind velocity is uncertain, workload demand is uncertain, failure occurs Deng these uncertain factors or event bring serious potential threat for the security and stability of system operation.Cause How this, count and these uncertain factors and event carry out power system fast and accurately time-domain-simulation, with the dynamic of analysis system Temporary characteristic (including transient stability, frequency shift (FS) etc.), has for the security and stability for promoting and improving system operation Significance.
The time-domain simulation method (hereinafter referred to as uncertain time-domain-simulation method) of meter and parameter uncertainty is main at present There are two kinds：Simulation and analytic method.Simulation is given birth to using the arbitrary sampling methods such as Monte Carlo Method, Latin hypercube method are included Into the simulation sample of substantial amounts, the dynamic temporary characteristic that output sample carrys out analysis system is then counted.The advantages of simulation is to calculate Method is simple, and shortcoming is that convergence rate is slow, it is necessary to which the sampling simulation sample of substantial amounts, it is very long to calculate the time.Analytic method is led to The time-domain-simulation of negligible amounts is crossed, probabilistic relation formula or the functional relation established between simulation result and uncertain parameter, from And quantify the uncertainty of simulation result.The advantages of analytic method is that its amount of calculation is much smaller relative to simulation, and shortcoming is meter Calculation method is relative complex, theoretical imperfection, still among further development.Because analytic method has amount of calculation is relatively small to dash forward Go out advantage, along with an important branch of uncertainty analysis inherently art of mathematics, various more perfect new algorithms and Theory emerges in an endless stream, and as it is theoretical further perfect, there are analytic method very big potentiality to be asked applied to large-scale Practical Project In topic.
Analytic method includes trace sensitivity method, interval algorithm and probability assignments method etc..Probability assignments method is multinomial according to broad sense Formula chaology sampled, and the emulation that fewer number is carried out on sampled point solves simulation result on uncertain parameter Polynomial function (hereinafter referred to as nondeterministic function), due to its with exponential convergence characteristic and with more preferable potentiality should For engineering in practice, more attention of researcher are received.Sparse probability assignments method combines sparse grid method and probability point With method, when handling higher-dimension uncertainty quantification problem, because utilizing sparse grid method combination each component samples of uncertain parameter Point, required sample size is reduced relative to traditional probability assignments method based on Tensor Method, to a certain extent can be with Effectively alleviate dimension calamity problem.But this method is using Gauss point as sampled point, because Gauss point set is non-nested type point set, Therefore high order sampling point set, which is closed, does not include low order time sampled point, and each uncertain parameter component in sparse probability assignments method The sampled point set of multiple orders is all have chosen, if high order sampling point set, which is closed, does not include low order time sampled point, sampling number Amount is increased with cumulative fashion, and total sampling number is added by each order set comprising element number.If sampled point set uses Nested so that low order time sampled point set is contained in the sampled point set of higher order time, and total sampling number is equal to choosing Element number in the highest order sampled point set taken, so as to greatly reduce total number of samples amount, can accordingly increase substantially meter Calculate speed.
The content of the invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide one kind is sparse based on improving The power system uncertainty time-domain-simulation new method of probability assignments method, compared with prior art, the inventive method are being kept not Under the calculation accuracy condition of certainty quantized result, required sample size is drastically reduce the area, uncertain time domain is improved and imitates True velocity, and can adapt to the Arbitrary distribution of uncertain parameters, can consider wind farm wind velocity in time-domain-simulation, The influences of the uncertain parameter for simulation result such as position occur for workload demand, failure.
The purpose of the present invention can be achieved through the following technical solutions：
A kind of power system uncertainty time-domain simulation method based on the sparse probability assignments method of improvement, it is characterised in that Uncertain parameter sampled point is calculated using Kronrod methods so that sampled point meets Nested property, dilute so as to be greatly reduced Sample size needed for probability assignments method is dredged, and can adapt to the Arbitrary distribution of uncertain parameters, considers time-domain-simulation The uncertainty of position occurs for middle wind farm wind velocity, workload demand and failure, estimates the uncertain of output variable in time-domain-simulation Function, expectation and variance；Comprise the following steps that：
(1) its Gauss point is calculated according to the probability distribution of uncertain parameter in time-domain-simulation；
If uncertain parameter x, the uncertain parameter x in time-domain-simulation be present is wind farm wind velocity, workload demand or event Barrier occurs any in position, it is necessary to first calculate its orthogonal polynomial, the i.e. required Gauss point of zero point of orthogonal polynomial；If its Zeroth order and single order orthogonal polynomial are respectively Φ0(x)=1, Φ1(x)=x+k, then by Recursive Solution equation below group, obtain N-th (n=1,2 ..., l+1, l are sparse grid method order, typically take l=2) rank orthogonal polynomial functions Φn(x):
Wherein：ρ (x) is uncertain parameter x weight function or probability density function, and it is orthogonal multinomial further to try to achieve each rank Formula zero point, that is, obtain the Gauss point of each uncertain parameter；
(2) the sampled point set that Gauss point obtains uncertain parameter in emulation is expanded；
(2.1), it is necessary to which expanding the Gauss point set forms nesting after step (1) obtains the Gauss point of uncertain parameter Type Gauss point set, nested Gauss point set are the sampled point set of required uncertain parameter；If the k of uncertain parameter is (at the beginning of k Initial value takes 1) rank Gauss point set { λ(1), λ(2)…λ(2u+1)2v point { λ of middle addition(2u+2),λ(2u+3),…λ(2u+2v+1)(original collection Conjunction includes 2u+1 point, v=u+1), obtain k+1 ranks nested and expand Gauss point set (including 2u+2v+1 point), collect after expansion Conjunction should meet following condition：
The solving equations λ being made up of v equation of equation 2 above(2u+2)、λ(2u+3)、…λ(2u+2v+1), this 2v solution is added to In k rank Gauss point sets, the k+1 ranks nested for obtaining uncertain parameter λ expands Gauss point set { λ(1),λ(2)… λ(2u+2v+1)}；
(2.2) if k ＜ l, continue the expansion of Gauss point set, make u:=u+v, v:=u+v+1, k:=k+1, goes to (2.1) continue to calculate, the otherwise expansion of end step (2) calculates；
Nested expands the sampled point set that Gauss point set is required nondeterministic function, because it is obtained for expansion, so The point set of each order is mutually nested.Each uncertain parameter component have chosen multiple orders in sparse probability assignments method Sampled point set, if high order sampling point set, which is closed, does not include low order time sampled point, sampled point quantity is increased with cumulative fashion Long, total sampling number is added by each order set comprising element number；If sampled point set uses nested so that low Order sampled point set is contained in the sampled point set of higher order time, and total sampling number is equal to the highest order chosen and adopted Element number in sampling point set, so as to greatly reduce total number of samples amount, it can accordingly increase substantially calculating speed.
(3) the sampled point set of multiple uncertain parameters is combined using sparse grid method, obtains uncertain time-domain-simulation Input sample set π (λ)：
Wherein i∑=i1+i2…+id, to indicate the order index of each sampled point set order, d is uncertain parameter vector λ dimension,Represent the i of j-th of component of uncertain parameterjRank nested expands Gauss point set,For tensor product operator, ∪ is set union symbol.
(4) carry out simulation calculation and obtain uncertain time-domain-simulation output sample set；
Power systems with nonlinear differential algebraic system equation group model is solved using implicit trapezoid method, each input sample is corresponding to be solved An output sample is obtained, exports sample setIt is represented by：
WhereinFor with input sampleCorresponding emulation tnMoment Input variable value；
(5) nondeterministic function of the computer sim- ulation output variable on uncertain parameter；
After sampling emulation terminates, according to uncertain letter of the output sample estimation simulation data variable on uncertain parameter Number, its form are：
Wherein r∑=r1+r2…+rd, i.e., each polynomial function Φ order and, fr, can be before for Polynomial Spectra coefficient Face step obtains exporting sample calculating fr：
Wherein For the r of λ j-th of componentjRank orthogonal polynomial square cum rights integrated value,For Jth ties up the gaussian coefficient of uncertain parameter.
(6) uncertain expectation and the standard deviation for quantifying to obtain output variable is carried out；
According to sparse probability assignments method characteristic, the expectation of output variable is obtained with variance by the coefficient in nondeterministic function：
So far the nondeterministic function of output variable, expectation and variance in uncertain time-domain-simulation are obtained, it is imitative so as to obtain The stochastic behaviour that true output y is influenceed by uncertain parameter λ.
Compared with prior art, the present invention has advantages below：
(1) present invention expands by using Kronrod methods to Gauss point so that the sampled point of uncertain parameter Set meets Nested property, and compared with the sparse probability assignments method of non-nested formula, method therefor of the present invention is keeping uncertain Under quantized result identical calculations precision conditions, sparse probability assignments method can be greatly reduced needed for sample size, accordingly may be used To improve uncertain time-domain-simulation speed.
(2) be can adapt in the present invention based on the uncertain time-domain simulation method for improving sparse probability assignments method not true The Arbitrary distribution of qualitative parameter, therefore wind farm wind velocity in time-domain-simulation, workload demand, failure can be considered position occurs The influence of the uncertain parameter for simulation result such as put, rapidly and accurately estimate the nondeterministic function of simulation data variable, it is expected And variance.
Brief description of the drawings
Fig. 1 is the schematic flow sheet of the present invention；
Fig. 2 is the schematic diagram for the experimental system for possessing 39 nodes in the embodiment of the present invention.
Fig. 3 is three kinds of uncertain quantization method output variable bound time domain variation diagrams.
Fig. 4 is the amount of calculation and computational accuracy comparison diagram of the inventive method and sparse probability assignments method result of calculation.
Embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with the technology of the present invention side Implemented premised on case, give detailed embodiment and specific operating process, but the application of the present invention is unlimited In following embodiments.
As shown in figure 1, the present embodiment provides a kind of uncertain time-domain-simulation side based on the sparse probability assignments method of improvement Method, including step：
S1, establish based on the uncertain time-domain-simulation input sample set for improving sparse probability assignments method：
S101, the Gauss point for calculating uncertain parameter：
Given deterministic parameter, including：Unit parameter, network topology structure and device parameter；Uncertain parameter λ probability Distributed data, including node load demand PNodeDistribution, wind farm wind velocity v distribution, failure occurs on set faulty line Position ξ distribution；Emulate total time ttotal；Simulation step length h；Fault type might as well be set as three-phase ground；The target of time-domain-simulation Output variable y is the angular velocity omega and generator rotor angle δ of all generators；Set sparse grid method order l.In 39 node system examples 5 uncertain parameters are set, i.e. uncertain parameter vector has 5 components, uncertain parameter probability distribution situation such as table 1 It is shown, wherein hypothesis wind speed obedience scale coefficient is 12, the Weibull distribution that form factor is 2.3.
The node system uncertain parameter probability distribution situation of 1 10 machine of table 39
Parameter name Distribution pattern Distributed area
The load power of node 4 (perunit value) Cutting gearbox [4.50,5.50]
The load power of node 8 (perunit value) Cutting gearbox [4.72,5.72]
The load power of node 20 (perunit value) Cutting gearbox [6.30,7.30]
The wind farm wind velocity of node 33 (m/s) Weibull distribution [0,25]
Position occurs for failure It is evenly distributed [0,1]
The Gauss point calculating process of uncertain parameter is：
If d dimension uncertain parameters be present, to some component x of uncertain parameter, if its orthogonal polynomial functions Φ0(x) =1, Φ1(x)=x+k, then obtaining n-th by Recursive Solution equation below group, (n=1,2 ..., l+1, l are sparse grid method Order, typically take l=2) rank orthogonal polynomial functions Φn(x):
Wherein ρ (x) is variable x weight function or probability density function, further tries to achieve each rank orthogonal polynomial functions zero The Gauss point of point, as uncertain parameter.
S102, expand the sampled point set that Gauss point obtains uncertain parameter：
The obtaining step of the sampled point set of uncertain parameter is：
A) uncertain parameter is set as d dimensional vector λ, in k (k initial values take 1) rank Gauss point set of its jth dimension variable2v point of middle addition(original set includes 2u+1 point, v= U+1), obtain k+1 ranks nested and expand Gauss point set (including 2u+2v+1 point), to make the point set algebraic accuracy reach most Height, corresponding polynomial2v-1 multinomial should be no more than with arbitrary number of times It is orthogonal, that is, meet following condition：
The solving equations being made up of v equation of equation 2 aboveThis 2v solution is added Into k rank Gauss point sets, λ is obtainedjK+1 ranks nested expand Gauss point set
If b) k ＜ l, continue the expansion of Gauss point set, make u:=u+v, v:=u+v+1, k:=k+1, goes to one Step, otherwise terminate to expand calculating.
C) each component for uncertain parameter λ is intended to expand as procedure described above, so as to obtain uncertain ginseng The 1 of each components of number λ to l+1 ranks nested expands Gauss point set, the sampled point set as uncertain parameter.
S103, the multiple uncertain parameters of combination sampled point set, obtain uncertain time-domain-simulation input sample collection Close：
Uncertain time-domain-simulation input sample set π (λ) calculation formula is：
Wherein i∑=i1+i2…+id, to indicate the order index of each sampled point set order,Represent uncertain parameter The i of j-th of componentjRank nested expands Gauss point set,For tensor product operator, ∪ is set union symbol.
S2, the uncertain quantization of progress obtain nondeterministic function, expectation and the standard deviation of simulation data variable：
S201：Calculate and obtain uncertain time-domain-simulation output sample set：
By each input sample in input sample set π (λ)(λ is abbreviated as below(k)) make Substituted into for λ values in the subordination principle of certainty time-domain-simulation, solved using numerical integration method, obtain it Corresponding rocking curve, is designated as As with input Sample λ(k)Corresponding tnMoment exports sample.Correspondingly, each t is formedn(n=1,2,3 ... ttotal/ h) moment output sample set Close, output sample set calculation formula is：
WhereinFor with input sampleCorresponding tnMoment emulates Input variable value, l are sparse grid method order, and d is uncertain parameter vector dimension.
The nondeterministic function of S202, computer sim- ulation output variable on uncertain parameter：
All orders are met into 0≤r∑≤l+1(r∑=r1+r2…+rdTo indicate each polynomial function order index) Orthogonal polynomialComponent function set：
Wherein subscript q isIn set Q (Φr(λ)) in sequence number, D is set Q (Φr (λ)) in element number.Simulation data variable is on the nondeterministic function of uncertain parameter：
WhereinFor Polynomial Spectra coefficient, its calculation formula is：
Wherein For the r of λ j-th of componentjRank orthogonal polynomial square cum rights integrated value, The gaussian coefficient of uncertain parameter is tieed up for jth.
S203, carry out uncertain expectation and the standard deviation for quantifying to obtain output variable：
Carry out the uncertain expectation for quantifying to obtain output variable is with variance calculation formula：
Above-mentioned mistake Nondeterministic function estimation expression formula, expectation and the variance of each output variable in each time step has been calculated in journey, defeated so as to obtain Go out the stochastic behaviour that y is influenceed by uncertain parameter λ.
Using the node system of 10 machine 39 as example system, it is assumed that be respectively adopted based on the sparse probability assignments method of improvement Uncertain simulation method, the uncertain simulation method based on Monte Carlo Method, the uncertainty based on sparse probability assignments method are imitated True method, calculating contrast is carried out to it, to verify the validity of context of methods.The node example topological diagram such as Fig. 2 of 10 machine 39, wherein No. 33 node generating sets replace with wind power plant unit model.Emulation total duration is 10s, it is assumed that 2s moment in simulations, node Three-phase ground short trouble occurs on 10 to 11 circuit, and failure is cut off after 0.2s.
If simulation data is generator G31, G32 angular velocity omega31、ω32Generator rotor angle between (perunit value) and G31, G32, G34 Poor Δ δ1=δ32-δ31、Δδ2=δ34-δ32(degree).The inventive method is respectively adopted and sparse probability assignments method is emulated not Certainty quantifies (taking identical sparse grid method order l=3), to carry out error analysis, is carried out in addition using Monte Carlo Method Emulation is uncertain to be quantified, and is set convergence precision as 0.1%, is carried out 13100 certainty time-domain-simulations altogether, calculated knot Fruit is considered as exact value.Its bound, the bound meter of three kinds of methods are represented using the desired value ± three times standard deviation of output variable Calculate result (E, σ are respectively its expectation and standard deviation) as shown in Figure 3.
As seen from Figure 3, it is very high with the exact value goodness of fit based on the simulation result of the inventive method, and compared to based on dilute Probability assignments method is dredged, more close to exact value (simulation result based on Monte Carlo Method), it is seen that its computational accuracy is higher. In order to more specifically compare the inventive method and sparse probability assignments method, computational accuracy index is defined below, and compare two kinds Amount of calculation and computational accuracy of the method under different sparse grid method orders.
Using Monte Carlo Method result of calculation as exact value, output variable x (x can be ω or Δ δ) computational accuracy is defined Index is：
Wherein h is simulation step length, NhFor it is total when step number,Respectively the inventive method or sparse probability point X is calculated in t with methodhThe desired value and standard deviation of time step,Represent to calculate using DSMC Obtained x is in thTime step expected value and standard deviation.
When taking different sparse grid method orders, the amount of calculation and computational accuracy of the inventive method and sparse probability assignments method Contrast is as shown in Figure 4.(transverse axis is sample size, and the longitudinal axis is computational accuracy index, contrasts two broken lines corresponding to two methods)
From fig. 4, it can be seen that the line chart of the inventive method is consistently higher than sparse probability assignments method, it is seen that it is in identical calculations The lower computational accuracy of amount is higher, and required amount of calculation is less when reaching identical calculations precision.By Fig. 3 and Fig. 4 comparing result, Demonstrate the validity of the inventive method.
Particular embodiments described above only to illustrate the invention realize effect, be not intended to limit the invention.It is all Modification, conversion and the improvement for any unsubstantiality made within the basic ideas and framework of method proposed by the invention, It should be included within protection scope of the present invention.

Claims (1)

  1. It is 1. a kind of based on the power system uncertainty time-domain simulation method for improving sparse probability assignments method, it is characterised in that to use Kronrod methods calculate uncertain parameter sampled point so that sampled point meets Nested property, so as to which sparse probability be greatly reduced Sample size needed for distribution method, and the Arbitrary distribution of uncertain parameters is can adapt to, consider wind-powered electricity generation in time-domain-simulation The uncertainty of position occurs for field wind speed, workload demand and failure, estimates the nondeterministic function of output variable, phase in time-domain-simulation Prestige and variance；Comprise the following steps that：
    (1) its Gauss point is calculated according to the probability distribution of uncertain parameter in time-domain-simulation；
    If uncertain parameter x, the uncertain parameter x in time-domain-simulation be present is wind farm wind velocity, workload demand or failure hair Any, it is necessary to first calculate its orthogonal polynomial in raw position, the zero point of orthogonal polynomial is required Gauss point；If its zeroth order with Single order orthogonal polynomial is respectively Φ0(x)=1, Φ1(x)=x+k, then by Recursive Solution equation below group, the n-th (n=is obtained 1,2 ..., l+1, l are sparse grid method order, typically take l=2) rank orthogonal polynomial functions Φn(x)：
    Wherein：ρ (x) is uncertain parameter x weight function or probability density function, further tries to achieve each rank orthogonal polynomial zero Point, that is, obtain the Gauss point of each uncertain parameter；
    (2) the sampled point set that Gauss point obtains uncertain parameter in emulation is expanded；
    (2.1), it is necessary to which expanding the Gauss point set forms nested Gauss after step (1) obtains the Gauss point of uncertain parameter Point set, nested Gauss point set are the sampled point set of required uncertain parameter；If the k of uncertain parameter (k initial values take 1) Rank Gauss point set { λ(1), λ(2)…λ(2u+1)2v point { λ of middle addition(2u+2), λ(2u+3)... λ(2u+2v+1)(original set includes 2u+ 1 point, v=u+1), obtain k+1 ranks nested and expand Gauss point set (including 2u+2v+1 point), gathering after expansion should meet such as Lower condition：
    The solving equations λ being made up of v equation of equation 2 above(2u+2)、λ(2u+3)、…λ(2u+2v+1), this 2v solution is added to k ranks height In this point set, the k+1 ranks nested for obtaining uncertain parameter λ expands Gauss point set { λ(1), λ(2)…λ(2u+2v+1)}；
    (2.2) if k ＜ l, continue the expansion of Gauss point set, make u：=u+v, v：=u+v+1, k：=k+1, go to (2.1) Continue to calculate, the otherwise expansion of end step (2) calculates；
    (3) the sampled point set of multiple uncertain parameters is combined using sparse grid method, obtains uncertain time-domain-simulation input Sample set π (λ)：
    Wherein i∑=i1+i2…+id, to indicate the order index of each sampled point set order, d is uncertain parameter vector λ dimension Number,Represent the i of j-th of component of uncertain parameterjRank nested expands Gauss point set,For tensor product operator, ∪ is collection Merge collection symbol；
    (4) carry out simulation calculation and obtain uncertain time-domain-simulation output sample set；
    Power systems with nonlinear differential algebraic system equation group model is solved using implicit trapezoid method, each input sample corresponds to solution and obtains one Individual output sample, export sample setIt is represented by：
    WhereinFor with input sampleCorresponding emulation tnMoment exports Variate-value；
    (5) nondeterministic function of the computer sim- ulation output variable on uncertain parameter；
    After sampling emulation terminates, nondeterministic function of the simulation data variable on uncertain parameter is estimated according to output sample, its Form is：
    Wherein r∑=r1+r2…+rd, i.e., each polynomial function Φ order and, fr, can be according to preceding step for Polynomial Spectra coefficient Obtain exporting sample calculating fr：
    Wherein For the r of λ j-th of componentjRank orthogonal polynomial square cum rights integrated value,For jth Tie up the gaussian coefficient of uncertain parameter；
    (6) uncertain expectation and the standard deviation for quantifying to obtain output variable is carried out；
    According to sparse probability assignments method characteristic, the expectation of output variable is obtained with variance by the coefficient in nondeterministic function：
    So far the nondeterministic function of output variable, expectation and variance in uncertain time-domain-simulation are obtained, it is defeated so as to obtain emulation Go out the stochastic behaviour that y is influenceed by uncertain parameter λ.
CN201710649712.XA 2017-08-02 2017-08-02 Based on the power system uncertainty time-domain simulation method for improving sparse probability assignments method Pending CN107657071A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108508866A (en) * 2018-03-21 2018-09-07 浙江大学 A kind of gigawatt extra-supercritical unit failure identification variables method based on sparse opposite discriminant analysis
CN111046606A (en) * 2019-12-11 2020-04-21 哈尔滨工业大学 Global time-varying sensitivity calculation method for electromagnetic relay life cycle

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
LIN GUANG等: "Uncertainty quantification in dynamic simulations of large-scale power system models using the high-order probabilistic collocation method on sparse grids", 《INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108508866A (en) * 2018-03-21 2018-09-07 浙江大学 A kind of gigawatt extra-supercritical unit failure identification variables method based on sparse opposite discriminant analysis
CN111046606A (en) * 2019-12-11 2020-04-21 哈尔滨工业大学 Global time-varying sensitivity calculation method for electromagnetic relay life cycle

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